A New Dynamic Stall Approach for Investigating Bifurcation and Chaos in Aeroelastic Response of a Blade Section with Flap Free-Play Section

Abstract

This paper investigates the effects of the unsteady nonlinear aerodynamic, plunge/pitch cubic nonlinearities, flap free-play nonlinearity, and coupled nonlinear aeroelasticity on the dynamics of the three-dimensional blade section. The dynamic stall model is developed based on the unsteady Wagner aerodynamics. Coupling the developed nonlinear aerodynamic model and nonlinear elasticity model results in the nonlinear aeroelastic model. The nonlinear aeroelastic equation of motion is converted into a state-space form. The resulting nonlinear state-space equation of motion is simulated by a standard Runge–Kutta algorithm in MATLAB. The proposed model is validated against test data of distinct two- and three-degrees-of-freedom studies and is compared to the ONERA model. Bifurcation diagrams show that there is distinct airspeed, in which the system experiences limit cycle oscillations (LCOs) or chaos. Both hysteresis air loads and structural nonlinearity make the system unstable at airspeed less than linear flutter speed. The nonlinearity of the structure causes supercritical pitchfork bifurcation. Elastic-aerodynamic nonlinearity interaction causes sub-supercritical bifurcation at the lower airspeed and chaotic motion at a higher airspeed. Furthermore, the effects of the initial condition on the response of the nonlinear aero-servo-elastic system are investigated by the Lyapunov exponent method.